Rounding numbers (Edexcel GCSE Maths): Revision Notes
Rounding numbers
Rounding is a way to make numbers simpler by reducing the number of digits while keeping the value close to the original number. You'll need to master different types of rounding for your GCSE maths exam.
What is rounding?
Rounding means making a number simpler by changing some digits to zero or removing decimal places. The key principle is looking at the digit immediately to the right of where you want to round.
The Golden Rule of Rounding: If the digit is 5 or more, round up. If the digit is less than 5, round down.
How to round using place value
When rounding any number, you need to identify the place value you're rounding to, then look at the digit immediately to the right:
- Find the place value column you want to round to
- Look at the digit in the next column to the right
- Apply the rounding rule (5+ rounds up, less than 5 rounds down)
Remember: You're always looking at the digit to the right of your target place value to make your rounding decision.
Rounding to decimal places
Decimal places (d.p.) refer to the number of digits after the decimal point.
To round to 1 decimal place:
- Look at the digit in the second decimal place (hundredths column)
- If it's 5 or more, round the first decimal place up
- If it's less than 5, keep the first decimal place the same
Worked Example: Rounding to 1 Decimal Place
Round 5.043 to 1 d.p.
Step 1: Look at the hundredths digit: 4
Step 2: Since 4 is less than 5, round down
Step 3: Answer: 5.0 (you must write the zero to show you've rounded to 1 d.p.)
Rounding to whole numbers
To round to the nearest whole number:
- Look at the digit in the tenths column (first decimal place)
- Apply the rounding rule
Worked Example: Rounding to Whole Numbers
Round 5.043 to the nearest whole number
Step 1: Look at the tenths digit: 0
Step 2: Since 0 is less than 5, round down
Step 3: Answer: 5
Significant figures
Significant figures (s.f.) are the meaningful digits in a number. You always start counting from the first non-zero digit on the left.
Rules for significant figures:
- Count from the first non-zero digit
- All non-zero digits are significant
- Zeros between non-zero digits are significant
- Leading zeros (at the start) are not significant
Worked Example: Rounding to Different Significant Figures
Round 27.05 to different significant figures:
To 1 s.f.:
- Look at the first non-zero digit (2), then at the next digit (7)
- Since 7 ≥ 5, round up to 30
To 2 s.f.:
- The first two significant digits are 2 and 7
- Look at the next digit (0). Since 0 < 5, answer is 27
To 3 s.f.:
- The first three significant digits are 2, 7, and 0
- Look at the next digit (5). Since 5 ≥ 5, round up to 27.1
Rounding numbers less than 1
When rounding numbers less than 1 to a given number of significant figures, you must remember an important rule:
Critical Rule: Do not count the zeros at the beginning (leading zeros) when working with numbers less than 1.
Worked Example: Rounding Numbers Less Than 1
Round 0.0085 to 1 s.f.
Step 1: The first non-zero digit is 8
Step 2: Look at the next digit: 5
Step 3: Since 5 ≥ 5, round up
Step 4: Answer: 0.009
Key exam tips
Exam Success Tips:
- Always show that you understand what you're rounding to by writing the appropriate number of decimal places or significant figures
- When rounding to decimal places, include trailing zeros to show the precision
- Check your answer makes sense - it should be close to the original number
- In real-world contexts, consider whether rounding up or down makes practical sense
Common mistakes to avoid
Watch Out For These Common Errors:
- Forgetting to include trailing zeros when rounding to decimal places
- Counting leading zeros as significant figures
- Rounding multiple times instead of rounding once from the original number
- Not identifying the correct place value to look at
Remember!
Key Points to Remember:
- Look to the right: Always examine the digit immediately to the right of where you're rounding
- 5 or more rounds up, less than 5 rounds down
- Significant figures start from the first non-zero digit
- Leading zeros don't count as significant figures
- Show your precision by including trailing zeros when rounding to decimal places